AIS - Fractional Differential Equations: Theory and Computations (2022)
Speakers and Syllabus
Syllabus:
| Name of the Speaker with affiliation | No. of Lectures | Detailed Syllabus |
| Prof. Amiya K. Pani Professor, Department of Mathematics, Birla Institute of Technology and Science, Pilani-Goa Campus, Goa |
6 | Fractional ordinary differential equations and properties, Numerical solutions, Time-fractional diffusion equations, Fractional diffusion, Linear fractional equations and their properties, Theoretical studies, sub-diffusion, Current trends in fractional derivatives, Finite-difference method for fractional ODEs. |
| Professor K. Sreenadh Department of Mathematics, Indian Institute of Technology Delhi, Delhi | 4 | First order differential equation and its integral representation, Picard's method of successive approximations, Picard's theorem of local-in-time well-posedness, Maximal interval of existence and continuation, Lyapunov stability. |
| Prof. Samir Karaa Department of Mathematics and Statistics, Sultan Qaboos University Muscat, Oman | 4 | Fractional calculus, fractional integral, Riemann-Liouville fractional derivative, Caputo fractional derivative, Mittag- Leffler function, Fractional order evolution equation, Laplace transform. |
| Prof. Varsha S. Gejji Department of Mathematics, Savitribai Phule Pune University, Pune |
6 | Cauchy-type problems for ordinary differential equations of fractional order, Existence and uniqueness of solutions to Cauchy-type problems for ordinary differential equations of fractional order with Riemann-Liouville fractional derivative. Solvability of Cauchy-type problems with Caputo fractional derivative. Maximal interval of existence and the concept of continuation of solutions. Stability estimates for fractional order differential equations. Blow-up criteria in fractional order differential equations. |
| Prof. Harsha Hutridurga Department of Mathematics, Indian Institute of Technology Bombay, Mumbai |
7 | Elementary properties of Hilbert spaces, Orthogonality, Riesz representation theorem, Orthonormal basis, Mathematical modeling of diffusion and fractional diffusion equation, Long time asymptotic behavior of diffusion equation, Integral representation, Regularity and smoothing properties of diffusion equation. |
| Dr Yubin Yan Department of Mathematics, University of Chester, UK |
6 | Numerical method for fractional order ordinary differential equations, Backward Euler method, Second-order backward difference methods, Convolution, quadrature, Error estimate, Finite difference method for solving fractional diffusion equation, High-order approximation of Caputo fractional derivatives, Adaptive and high-order scheme for non-integer order differential equations. |
| Prof. Kapil K. Sharma Department of Mathematics South Asian University | 1 | Numerical method for ordinary differential equations |
| Dr. Navnit Jha Department of Mathematics South Asian University |
2 | Numerical method for heat equation. |
References:
- Bangti Jin, Fractional Differential Equations, An Approach via Fractional Derivatives, Springer
- A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier
Time Table
Time-Table (with names of speakers and course associates/ tutors):
|
Day |
Date |
Lecture 1 (9.30–11.00) |
Tea (11.05 –11.25) |
Lecture 2 (11.30–1.00) |
Lunch (1.00–2.00) |
Lecture 3 (2.00–3.30) |
Tea (3.35-3.55) |
Tutorial (4.00-5.00) |
Snacks 5.05-5.30 |
|
|
|
(name of the speaker |
|
(name of the speaker) |
|
(name of the speaker |
|
(name of the speaker |
|
|
Mon |
12-12-22 |
L1 K. Sreenadh |
|
L2 Samir Karaa |
|
L3 K. Sreenadh |
|
T1 KS, SKS, YS |
|
|
Tues |
13-12-22 |
L4 K. Sreenadh |
|
L5 Varsha Shridhar Gejji |
|
L6 Samir Karaa |
|
T2 VSG, KS, YS |
|
|
Wed |
14-12-22 |
L7 Varsha Shridhar Gejji |
|
L8 Samir Karaa |
|
L9 Varsha Shridhar Gejji |
|
T3 VSG, SK,NJ |
|
|
Thu |
15-12-22 |
L10 Varsha Shridhar Gejji |
|
L11 Samir Karaa |
|
L12 Yubin Yan
|
|
T4 VSG, NJ, PM |
|
|
Fri |
16-12-22 |
L13 Varsha Shridhar Gejji |
|
L14 Varsha Shridhar Gejji |
|
L15 Yubin Yan |
|
T5 YY, PM, NK |
|
|
Sat |
17-12-22 |
L16 Kapil K. Sharma
|
|
L17 K. Sreenadh |
|
L18 Yubin Yan |
|
T6 YY, PM, NK |
|
|
SUNDAY: OFF |
|||||||||
|
Mon |
19-12-22 |
L19 Harsha Hutridurga |
|
L20 Harsha Hutridurga |
|
L21 N. Jha |
|
T7 HH,NJ, RKP |
|
|
Tues |
20-12-22 |
L22 Harsha Hutridurga |
|
L23 Harsha Hutridurga |
|
L24 N. Jha |
|
T8 HH, NJ, RKP |
|
|
Wed |
21-12-22 |
L25 Amiya K. Pani |
|
L26 Amiya K. Pani |
|
L27 Harsha Hutridurga |
|
T9 HH, NJ, RKP |
|
|
Thu |
22-12-22 |
L28 Harsha Hutridurga |
|
L29 Amiya K. Pani |
|
L30 Yubin Yan |
|
T10 AKP, PD, TM |
|
|
Fri |
23-12-22 |
L31 Harsha Hutridurga |
|
L32 Amiya K. Pani |
|
L33 Yubin Yan |
|
T11 AKP, PD, TM |
|
|
Sat |
24-12-22 |
L34 Amiya K. Pani |
|
L35 Amiya K. Pani |
|
L36 Yubin Yan |
|
T12 AKP, PD, TM |
Valedictory and feedback session
|
Tutorial Assistants:
|
S. No. |
Name |
Affiliation |
|
1 |
Dr. Navnit Jha |
Department of Mathematics, South Asian University, New Delhi |
|
2 |
Dr. Saroj K. Sahani |
Department of Mathematics, South Asian University, New Delhi |
|
3 |
Dr. R. K. Pandey |
Department of Mathematics, Indian Institute of Technology (BHU) Varanasi |
|
4 |
Dr. P. Danumjaya |
Department of Mathematics, BITS Pilani-K K Birla Goa Campus, Goa |
|
5 |
Dr. T. Mathur |
Department of Mathematics, BITS, Pilani, Rajasthan |
|
6 |
Dr. Pankaj Mishra |
Department of Mathematics, Deshbandhu College, University of Delhi, New Delhi |
|
7 |
Dr. Neelesh Kumar |
Department of Mathematics, Sri Venkateswara College, New Delhi. |
|
8 |
Dr. Yashi |
Shaheed Rajguru College of Applied Sciences, University of Delhi, Delhi |
Full forms for the abbreviations of speakers and tutors:
HH: Harsha Hutridurga, KS: K. Sreenadh, VSG: Varsha Shridhar Gejji, AKP: Amiya K. Pani,
KKS: Kapil K. Sharma, SK: Samir Karaa,YY: Yubin Yan, PD: P. Danumjaya,NJ: Navnit Jha,
RKP: R. K. Pandey, SS: Saroj K. Sahani, TM: T. Mathur, PM: Pankaj Mishra,
NK: Neelesh Kumar, YS: Yashi